test rig for applied experimental investigations of the thermal...

Test Rig for Applied Experimental Investigations of theThermal Contact Resistance at theBlade-Rotor-Connection in a Steam TurbineDennis Toebben1*, Xavier E. R. de Graaf1, Piotr Luczynski1, Manfred Wirsum1, Wolfgang Mohr2, KlausHelbig3

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2017

InternationalSymposium on

Transport Phenomenaand

Dynamics of RotatingMachinery

Maui, Hawaii

December 16-21, 2017

AbstractStudies have shown that in a pre-warming respectively warm-keeping operation of a steam turbine,the blades and vanes transport most of the heat to the thick-walled casing and rotor. �ereby,a bo�le-neck arises at the connection between the blade root and the rotor. �e contact heatresistance at these interfaces a�ects the temperature distribution and thus the thermal stresses inthe rotor. �e present paper introduces a thermal contact resistance test rig, which is designed toquantify the contact heat transfer at the blade-rotor-connection of a steam turbine. An uncertaintyanalysis is presented which proves that the average measurement uncertainties are less than onepercent. In addition to the test rig, a numerical model of the specimen for the determinationof the thermal contact resistance is developed and introduced. Results of several steady-statemeasurements under atmospheric and evacuated atmosphere using a highly temperature-resistantchromium molybdenum steel are shown. As a main in�uence parameter the contact pressure isinvestigated, which is a�ected by the rotational speed of the turbine. �e investigations show asigni�cant contact heat resistance especially at small contact pressures.KeywordsContact Heat Transfer – Steam Turbine – �ermal Contact Resistance1Institute for Power Plant Technology, Steam and Gas Turbines, RWTH Aachen University, 52062 Aachen, Germany2General Electric (Switzerland) GmbH, Brown Boveri Str. 7, 5401 Baden, Switzerland3General Electric Power AG, Boveristraße 22, 68309 Mannheim, Germany*Corresponding author: [email protected]

INTRODUCTION

Steam turbines in conventional power plants are increasinglystrained due to the growing demand of �exible operation.Especially frequent and fast start-up sequences lead to highthermal stress within the thick-walled components like therotor and the casing. �e temperature gradients within thesolid structures which are in�uenced by the heat transfercoe�cients at the surfaces are responsible for these highthermal stresses. Before the steam turbine is synchronizedwith the grid, the heavy components need to be pre-warmed.In a conventional operation superheated steam is used forheating up the steam turbine. Other approaches use hot air,for example to keep the turbine warm or to pre-warm it. Insuch a operation, the main heat transfer between the main�ow and the structure arises at the surfaces of the blades andvanes [1]. �e heat, being conducted to the rotor and thecasing, has to pass the contact surfaces between the bladeand rotor respectively the vane and the casing. �ese contactsurfaces constitute a kind of bo�le-neck for the heat transportwhich a�ects the temperature gradients and consequentlythe thermal stress.

A recent study [2] show that the contact conductancehas a signi�cant in�uence on the stress amplitude withinthe steam turbine rotor. A few experimental and analyticalapproaches for the determination of the thermal contact re-

sistance (TCR) are known from literature. Fenech, Rohsenow,Mikic, and Yovanovich are pioneers in research on TCR-topics ([3], [4], [5]). �e �rst investigations were conductedbased on research on spacecra� and other space vehicles. Abasis for further analytical approaches provide Cooper etal. [6]. �ey developed a calculation model for conforming(nominally �at) rough surfaces. A detailed overview on theresearch done on this �eld from 1965 to 2005 is made byMadhusudana [7]. �e latest summary regarding TCR wasreleased in 2014 in the second edition of the book thermalcontact conductance wri�en by [8]. Ustinov et al. ([9] & [10])developed a new model for calculating the real contact area.�e experimental values provide the dependence of the TCRon roughness, material structure and the contact pressure.�e results o�er an explanation for the large discrepanciesthat exist between the data of several authors. Burghold et al.[11] introduce a method to measure contact heat transfer co-e�cients by means of transient temperature measurements.In these transient measurements an oscillation was observedfrom which a hysteresis e�ect arose.

In the present paper a method for applied experimentalinvestigations of the TCR at the blade-rotor-connection ina steam turbine is presented. In the �rst part of the paper,the test rig and the numerical specimen model is introducedwith a detailed explanation of the boundary conditions. Sub-sequently, the measurement values are discussed in an un-

Test Rig for Applied Experimental Investigations of the Thermal Contact Resistance at the Blade-Rotor-Connection in aSteam Turbine — 2/9

certainty analysis. �e third part shows �rst measurementsof the temperature at 26 di�erent measurement positionswithin the specimen by variation of the contact pressure andthe heat �ux. In the last part of the present paper the TCR isdetermined by use of the numerical model and based on theexperimental results.

NOMENCLATURESymbolsA AreaGr Grashof-numberRa Rayleigh-numberPr Prandtl-numberp Pressureg Gravityn Rotational speedÛQ Heat �ux

T TemperatureT̄ Average temperature

Greekα Heat transfer coe�cientβ Expansion coe�cientδ Gap width∆ Di�erenceη Dynamic viscosityλ �ermal conductivityϑ Relative temperature di�erence

Abbreviationsatm Atmospheric ambient pressureAP Air pocketBRC Blade-Rotor-ConnectionCHT Conjugate Heat TransferCI Contact interfaceFEM Finite Element Methodrel. err. Relative errorTCR �ermal Contact ResistanceT1 - T26 �ermocouplesU95.4 Interval with 95.4 % level of con�dencevac Evacuated ambient pressure

Subscripts0 Referencec Contactcool CoolingH Heating plane (average of T1 & T4)HC Heating cartridgeR Reference thermocouple for calibration

1. TEST RIGFigure 1 shows the test rig, which is designed for the measure-ment of the thermal contact resistance (TCR) at the contactareas of a turbine blade. Di�erent designs of blade or vaneroots can be investigated. �e test rig o�ers the possibility to

analyze the in�uence of the rotational speed (i.e. contact pres-sure), the ambient pressure and the contact surface properties(e.g. roughness, oxidation layer, lubricant). Furthermore, theradiation in�uence via the air pockets, which are locatedbetween the contact surfaces can be investigated. �e TCRis calculated according to Eq. (1) in which ÛQc is the heat �uxthrough the contact surface Ac and ∆Tc is the temperaturedi�erence between the area averaged temperatures of bothsurfaces which are in contact.

TCR =∆Tc Ac

ÛQc

=1αc

(1)

Figures 1 and 2 illustrate the single components of the test rig.�e key component is the traction system (1) in which thespecimen is installed. �e traction system is located withina pressure chamber (2). By evacuating the surrounding airwithin this chamber, the heat losses can be minimized. Inaddition, the pressure chamber provides the opportunity toinvestigate the impact of the ambient pressure on the contactheat transfer by pressurizing. �e hydraulic system (3) servesto adjust the traction force and thus the contact pressure. �eperistaltic pump (4), the air cooler (5) and the tempered watertank (6) belong to the cooling system. �e air cooler dissipatesthe heat absorbed from the specimen. A tempered water tankand the peristaltic pump ensure the reproducibility of themeasurement. Component (7) is a monitored oil bath inwhich the reference thermocouples are located.

Figure 3 shows the installed specimens. �e experimentalset-up consists of two parts. A blade specimen and a rotorspecimen with its blade groove are installed in this con�g-uration . During the test, the specimens are surrounded byan additional casing faced by high temperature insulation toreduce radiation heat losses. �e blade specimen is heatedup by two heating cartridges at the top in a horizontal plane.

1

2

3 45

6

7

1: Traction system2: Pressure chamber (Ground plate)3: Hydraulic system4: Peristatic pump5: Air cooler6: Tempered water tank7: Reference thermocouples

Figure 1. CAD model


A heat �ux from the top of the blade to the rotor specimen isgenerated by a cooling drill at the bo�om of the rotor spec-imen, through which cooling water is pumped. �e rotorspecimen is �xed at the bo�om. Whereas, above the heatingcartridges the traction force is transmi�ed. �e traction forceis provided by a hydraulic stamp and measured by a load cellbelow the �xed baring.

Figure 4 illustrates the supply scheme. During the test amultitude of measurements are collected. 26 Type-N thermo-couples in total are used for the measurement of the temper-

2

75

6

4

3

Figure 2. Test rig

Heating Cartridge

Cooling

Blade Specimen

Rotor Specimen

Tension Bracket

Fixed Baring

Load Cell

Force

Figure 3. Installed specimens

ature distribution inside the specimen. �ese measurementsignals are transmi�ed through the pressure chamber. Eachmeasurement signal is compensated by a reference measure-ment in a oil bath which is monitored by a PT-100 thermo-couple. �e traction force is measured by a calibrated loadcell as mentioned before. To monitor the boundary condi-tions within the pressure chamber the temperature and thepressure is measured. �e temperature of the water tank aswell as the temperature of the heating cartridges are recordedto control the supply system. For a high accuracy the com-plete measurement chain in the �nal experimental set-upincluding the data logging system, ducts and compensationis calibrated. �e measurement points are shown in Fig. 5.�e upper four (pair 1) and the lower six measurement points(pair 7) are used to measure the heat input and output. Due tobalancing the energy �ow in this way, a higher accuracy canbe achieved compared to the measurement of the power in-put by the heating cartridges (which is a�ected by heat lossesthrough the traction rod) and the temperature di�erence be-tween inlet and outlet of the cooling water. �emeasurementpoints of pair 2 to 5 are used to determine the thermal contactresistance. All other temperature measurements are used toinvestigate the heat transfer through the air pockets and tovalidate the numerical model which is shown in Fig. 6. �erelevant test rig and material properties are summarized inTable 1.

T

T

p

F

T

+-

Air Cooler

Tempered Water Tank

Peristatic Pump

Load Cell

Specimen

Stamp

Hydraulic System

Cooling System

Data Logging System

Venting System

Heating Cartridge

Insulation

Pressure Chamber

TractionSystem

Figure 4. Supply scheme


Table 1. Test rig and material properties

Contact pressure (max.) 100 [MPa]Average temperature at CS 100 - 300 [◦C]Ambient pressure 30 - 3000 [mbar]Heating input (max.) 630 [W]Conductivity (20 - 650 ◦C) 24 - 29 [W/m/K]Surface roughness (Rz ) 6.4 [µm]Used material X22 CrMoV 12-1

Both the blade and the rotor specimen are made of thesame material (Table 1), which is heat resistant under highload. �is material is similar to the material which is used inmodern high and intermediate pressure steam turbines. �egeometry of the blade has been modi�ed to enable heat inputand the tensile strength. For the design of the specimen, nu-merical Finite Element Methods (FEM) and Conjugate HeatTransfer (CHT) calculations were used to optimize the stabil-ity, the homogeneity of temperature and the heating up time.�e blade root design is straightened, however, the contactsurfaces represent the original design.

2. NUMERICAL MODEL & ANALYSIS�ere are three reasons for building-up the numerical modelof the specimen: Support in the design process, investigationof the heat transfer mechanisms between blade and rotor andin a further step the validation as well as development of acontact heat transfer correlation.

T11T9 T8 T6

T15

T16

T12T20T14

T13 T19

T17T18T7

T3T10

T4

T5 T2

T1

T23 T21 T22

T24 T25 T26

1

2 3

4 56

7

Figure 5. Measurement positions

During the design process the numerical model was usedto design the required heating and cooling conditions and tosecure the mechanical stability of the specimen by simulationof the mechanical and thermal induced stresses. In a nextstep, the geometry parameters were optimized. �e width ofthe specimen conforms with the axial distance between twoneighboring repetitive stages. �e length of the rotor and theblade specimen was calculated to �nd an optimum regardinga uniform temperature distribution in the horizontal planesof pair 1 and pair 7 - which guarantees a minimal error inthe energy balance - as well as regarding the heating uptime or rather the total surface area which a�ects the heatlosses to the ambient. Subsequently, the numerical modelwas used to �nd suitable measurement points close to thecontact surface but simultaneously with a high temperaturedi�erence between opposed measurement points to minimizethe relative measurement error. For that purpose, analyticalapproaches for the determination of the TCR from literature[6] were integrated into the numerical model.

Two di�erent numerical models exist. A CHT modelin ANSYS CFX (Fig. 6) to calculate the heat �uxes and thetemperature distribution. �e results of these calculationsserve as an input parameter for the second model in ANSYSMECHANICAL which uses Finite Element Methods (FEM)to calculate the thermal and mechanical stresses and the re-sulting deformation. Two di�erent types of meshes of thesolid body are used. A tetrahedral mesh including the ther-mocouple holes and a hexahedral mesh without these holes.Both models use temperature-dependent material propertiesof the steel and data based �uid properties (IAPWS Libary).�e SST turbulence model is used for the simulation of thecooling.

For the present investigations a hammer-head blade rootdesign (Fig. 6) is used. �is blade root design has four contactinterfaces, two in axial direction (CI1a & CI1b) and two inradial direction (CI2a & CI2b). Between the blade root andthe rotor as well as between the axial (CI1) and radial (CI2)

250

50

500

T [°C]AP1 AP2

AP3

CI1a CI1b

CI2a CI2b

Figure 6. CHT simulation with hexahedral mesh (le�),hexahedral mesh (center), contact interfaces (CI) and airpockets (AP) (right)


contact areas air pockets can be found. Within theses airpockets heat transfer due to thermal convection, conductionand radiation occurs. For the investigation of the impact ofthermal convection the Rayleigh-number (Ra) is calculatedusing Eq. (2).

Ra = Gr · Pr =βgρ2 | ∆T | δ3

η2 ·ηcpλ

(2)

In Eq. (2) the expansion coe�cient is evaluated as β = 1/T̄AP

and δ is the gap width of the air pocket between blade rootand rotor groove. Based on the assumption of an averageair temperature of T̄AP = 250◦C within the air pockets andthe temperature di�erence between the enclosed air and theaverage contact surface temperature of ∆T = 50K (in a con-servative estimation), the Rayleigh-number is calculated toRa = 3.163. Because of such a low Rayleigh-number it isassumed that thermal convection can be neglected as shownin [12]. For the calculation of the heat transfer by conductionand radiation through the air pockets, a separate mesh forthese cavities is generated as shown in the right chart ofFig. 6. For a higher stability of the numerical simulation, theair pockets are de�ned as solid bodies with the transparencyand conductivity of air depending on the average air proper-ties. Figure 7 shows the in�uence of the thermal conductionand the heat radiation through the air pockets on the totalheat transfer from blade to rotor ( ÛQtotal). �e calculationsare conducted with constant temperature at the heat source(THC = 500◦C) and at the heat sink (TCool = 30◦C). Withincreasing TCR ( Eq. (1)) the impact of heat radiation andconduction through the air exponentially increases. WithTCR → 0 the heat transfer through the air pockets ( ÛQAP)related to the heat transfer through the contact interfaces( ÛQc) is about 9% for radiation as well as conduction and about5% for only radiation (Fig. 8). �e e�ect of heat radiationgrows with increasing average temperature level T̄AP andalso with increasing temperature di�erence of the surfacesin contact.

During a warm-keeping or a pre-warming process, verylow rotational speeds of the turbine rotor are possible, de-pending on the turning engine. In this case, low centrifugalforces as well as low contact pressures occur resulting in highTCRs. �us, the heat radiation and the conduction throughthe AP have to be considered.

3. UNCERTAINTY ANALYSISIn order to quantify uncertainties of the measured data, thefull measuring chain has to be analyzed. �is analysis is con-ducted based on the “guide to the expression of uncertaintyin measurement” [13].

�e uncertainty analysis can be divided into two parts.�e �rst part includes all 26 Type-N thermocouples mountedon the specimen. �e upper 20 thermocouples (pairs 1–6 inFig. 5) are calibrated in a temperature range of 100◦C−500◦C.�e lower 6 thermocouples (pair 7) are calibrated in a temper-ature range of 40◦C−90◦C. In accordance to [14], the calibra-tion is performed through a polynomial �t of 7th degree. Con-

sequently, every thermocouple has individual parameters. Af-ter the calibration, the thermocouples are compared througha reference measurement at three temperature points. �isreference measurement enables to identify temperature dif-ferences between thermocouples a�er the calibration. �earrangement of thermocouples in groups with the lowesto�set temperature between each other, enables to achievea very low relative measurement uncertainty (Table 2). �eapproach to examine the relative measurement uncertaintyinstead of the absolute measurement uncertainty based on[13] is legitimate, due to the use of temperature di�erencesfor determination of the thermal contact resistance. 4TR,i de-scribes the maximum temperature di�erence at all reference

10-5 10-4 10-3 10-2 10-1

TCR [m2K=W ]

10-2

10-1

100

_ Qto

tal=

_ Q0;C

HT

[-]

AdiabaticRadiationRadiation + Conduction

10-5 10-4 10-3 10-2 10-1

TCR [m2K=W ]

10-2

10-1

100

_ QA

P=

_ Qc[-]

RadiationRadiation + Conduction

Figure 7. Total heat transfer from blade to rotor regardingdi�erent heat transfer phenomena through the air pockets(CHT model THC = 500◦C, TCool = 30◦C)

10-5 10-4 10-3 10-2 10-1

TCR [m2K=W ]

10-2

10-1

100

_ Qto

tal=

_ Q0;C

HT

[-]

AdiabaticRadiationRadiation + Conduction

10-5 10-4 10-3 10-2 10-1

TCR [m2K=W ]

10-2

10-1

100

_ QA

P=

_ Qc[-]

RadiationRadiation + Conduction

Figure 8. Heat transfer through the air pockets related tothe contact heat transfer (CHT model THC = 500◦C,TCool = 30◦C)


measurement points of pair i. �e term 4T̄min,i indicates theminimum temperature di�erence within pair i throughoutthe operating range of the test rig. So, the stated relative error(4TR,i/4T̄min,i) in Table 2 represents the maximum relativeerror of the thermocouple pairs.

Table 2. Absolute and relative error of thermocouplesmounted on the specimen

4TR,i [K] 4T̄min,i [K] rel. err. [%]Pair (1–7)∗ 0.515 88.346 0.583Pair 2 0.064 40.935 0.156Pair 3 0.089 42.24 0.211Pair 4 0.028 15.708 0.178Pair 5 0.094 17.353 0.542Pair 6 0.014 45.01 0.031∗Di�erence between pair 1 and pair 7.

�e second part of the uncertainty analysis includes everymeasurement equipment used to monitor the experimentaltest rig. �is equipment is also used to reproduce certainmeasurement points during series of measurements. Table 3shows that the temperature level (THC ) can be reproducedin a range of 4.7 K in maximum. �e reproducibility of thetensile force has a maximal relative error of 1.01% and thePT100 has an uncertainty of 0.243 K.

Table 3. Uncertainty analysis of remaining measurementequipment

Measurement range U95.4 rel. err.PT100 [◦C] 18 – 30 0.243 1.35 %THC [◦C] 210 – 550 4.664 2.22 %p [mbar] 30 – 1030 0.401 1.34 %pc [MPa] 4.75 – 95.25 0.048 1.01 %

�e higher measurement uncertainty of the temperaturelevel of the heating cartridge is negligible since it is only usedas a security measurement to avoid the overheating of theheating cartridges. In order to achieve reproducible heatingtemperatures, the thermocouples in the upper level of pair 1are monitored. Uncertainty in overall measurement resultscan be induced by the measurement equipment itself, asanalyzed above, but also by uncertainties of the measurementprocedure.

�e �rst series of measurements consist of 54 operatingpoints (Table 4), varying each the ambient pressure (atm,vacuum (∼ 30 mbar)), the traction force (pc) and the referencetemperature at upper level of pair 1 (TH ). All measurementsare steady-state. During the measurement 60 data pointswere collected within a time period of �veminutes and �nallyaveraged. To analyze the impact of the ambient pressure onthe heat transfer, the pressure in the surrounding atmospherecan be varied. Due to the variation of the contact pressure thee�ect of increasing rotational speed of the turbine rotor canbe simulated and investigated. �e variation of the heating

temperature enables the simulation of a heating up procedureand to analyze heat radiation in�uence.

Table 4. Measurement schedule

pamb atm, vacuumTH [◦C] 150, 250, 350pc [kN] 0.5, 1.5, 2.5, 3.5, 5.0, 6.5, 7.5, 9.0, 10.0

To prove the steady state measuring conditions, the tem-perature di�erence between thermocouple T4 and T5, as aparameter for the entering heat �ux is provided in Fig. 9. �istemperature di�erence �uctuates in a very narrow range upto 0.05 K, which is within the band of measurement errorsinduced by the thermocouples. Hence, the time averagedmeasurement results can be assumed as steady-state.

4. RESULTS & DISCUSSION�e �rst series of measurements, which is presented in thissection, was conducted with a simpli�ed blade specimen. Toinvestigate the in�uence of the contact pressure isolated fromother in�uences induced by the axial contact interfaces (CI1),these contact areas were removed. Consequently, the inves-tigated blade specimen only has the radial contact interfaces(CI2).

For the evaluation of the measurement results, a dimen-sionless temperature is de�ned in Eq. 3. �is temperature ϑis the average temperature di�erence of the radial contactsurfaces ∆T̄CI2, referenced on the temperature di�erence atthe top and the bo�om of the specimen (pair 1 - pair 7).

ϑ =∆T̄CI2

T̄Pair1 − T̄Pair7(3)

Figure 10 illustrates the measurement results as compara-tive temperature di�erence ϑ on the Y-Axis over the contact

Number of measurements0 10 20 30 40 50 60

"T

CI2[K

]

155.3

155.35

155.4

155.45

155.5

155.55

T13-T14

Number of measurements0 10 20 30 40 50 60

"T[K

]

15.22

15.23

15.24

15.25

15.26

15.27

15.28

T4-T5

Figure 9. Temperature �uctuation over time between themeasurement positions T4 & T5


pressure pc at the contact interface CI2 respectively the equiv-alent rotational speed n (n ∝ p0.5

c ). �e measurements withatmospheric ambient pressure are represented by a continu-ous line and that ones with evacuated atmosphere by a dotand dash line. �e di�erent temperature levels (TH [◦C]) arecharacterized by separate marker types and colors.

�e expected global trend is a decrease in the contact tem-perature di�erence ϑ with increasing contact pressure. Bothvalues of ϑ (atm & vac) decrease with increasing temperaturelevel, which indicates the heat radiation in�uence. At lowcontact pressure, the impact of the air pockets is signi�cant asshown before in Fig. 8. �is corresponds to the atmosphericresults which show a clear temperature level dependency atlow contact pressures due to conduction and heat radiation.�e impact of the heat radiation increases with both, the tem-perature level and the temperature di�erence between theopposite surfaces. However, with increasing contact pressure,the air pockets lose impact due to the predominant e�ectof the metal conduction. At the highest measured contactpressure, the measurement results are very close.

In contrast to the very homogeneous trend of the atmo-spheric measurements, the results under an evacuated atmo-sphere show an increased sca�er. It has been observed thatthe temperature distribution of the specimen is very sensitiveon changes in the pressure level close to vacuum. Duringthe measurements the pressure inside the pressure chamberhas �uctuated around 3%. �e used vacuum pump is able toevacuate the pressure chamber on an absolute pressure levelof 28 mbar, but without a regulation. �is can be a reasonfor the inhomogeneous measurement results. However, thegeneral trend of both, atmospheric and evacuated ambientpressure, is similar.

Contact pressure [MPa]0 20 40 60 80 100

#[!

]

0.1

0.2

0.3

0.4

0.5

0.6

0.7atm, T

H=150

atm, TH

=250

atm, TH

=350

vac, TH

=150

vac, TH

=250

vac, TH

=350

Rotational speed [rpm]0 3000

Figure 10. Average dimensionless temperature di�erencesϑ at contact interface CI2

At low contact pressure the di�erence of ϑ between thetwo pressure levels is high because of the high impact of theair pockets and thus, of the ambient pressure. Concerningan evacuated atmosphere it can be assumed that the heattransfer by conduction is negligible. Hence, the remainingheat transfer phenomenon is heat radiation.

Figure 11 shows the overall heat �ux through the speci-men depending on the contact pressure. �e inlet heat �ux,which is illustrated by a continuous line, is calculated by thetemperature di�erence at pair 1 and the outlet heat �ux (dotand dash line) is calculated by the temperature di�erenceat pair 7. Both of them are calculated with a temperaturedepending thermal conductivity. Atmospheric and evacuatedambient pressure measures can be di�erentiated by di�erentline colors.

As a general trend it can be observed that the heat �uxincreases with increasing contact pressure and thus, withdecreasing TCR. �is e�ect is enhanced by the temperaturelevel. �e absolute heat losses - the di�erence between inletand outlet - of the measurements with atmospheric pres-sure also increase with increasing temperature level. �ise�ect can mainly be traced to the increasing heat �ux, sothat the relative heat losses are primary independent on thetemperature level. �is underlines the e�ect of the insula-tion surrounding the specimen. �e heat losses at evacuatedambient pressure con�rm this observation. �e red lines inFig. 11 are nearly matching, no ma�er the temperature level.At low contact pressure, the outlet heat �ux is slightly abovethe inlet heat �ux. �is is within the range of measurementerror.

5. THERMAL CONTACT RESISTANCEFor the determination of the thermal contact resistance thenumerical FEMmodel as well as an one dimensional approachare developed.

A FEM model with integrated thermocouple holes andtetrahedral mesh (Fig. 12) is used for the numerical investi-

0 50 100Contact pressure [MPa]

0

0.2

0.4

0.6

0.8

1

_ Q=

_ Q0[!

]

in, atm, TH=150

out, atm, TH=150

in, atm, TH=250

out, atm, TH=250

in, atm, TH=350

out, atm, TH=350

in, vac, TH=150

out, vac, TH=150

in, vac, TH=250

out, vac, TH=250

in, vac, TH=350

out, vac, TH=350

Figure 11. Incoming and outgoing heat �uxes for di�erentmeasurement series


gation. As boundary conditions, an average temperature ofpair 1 is set at the upper and of pair 7 at the lower wall. Allother surfaces except for the contact surfaces (CI2) and thesurfaces of the air pockets are set adiabatically. Within theair pockets, the radiation heat �ux and the conduction heat�ux through the air is considered. At the contact surfaces,an initial TCR is de�ned. �is TCR is adapted in an itera-tive process, in which the solver minimizes the error at thetemperature measurement positions T9, T11, T14 and T15.�ese values are set based on the measurements. All othertemperatures are calculated. A result is illustrated in Fig. 12(pc = 4.8 MPa, vac, TH = 150◦C). It can be observed that theblade specimen has a clearly higher temperature than therotor specimen. �e traction force F = 4.8MPa is quite low.�us, the TCR is high as well as the temperature di�erencebetween the contact surfaces.

�e FEM model is able to recompute the temperaturedistribution in good accordance with the measurement data.�e maximal deviation averaged for the measurement seriesis 2◦C.

For the examination of the TCR, also a simpli�ed one-dimensional (1D) approach is used and compared with theresults of the FEM model (Fig. 13). �e 1D model combinedwith a TCR correlation, which will be developed, enables thefast and simple calculation of the heat which is conductedfrom the blades to the rotor of a steam turbine. For the 1Dapproach it is assumed that the heat is transferred only inone dimension, orthogonally to the contact surface between

T/T0 [K/K]

T23 T21

T19

T18

T22

T7

T3T10

T15

T11

T14

T9

T13 T16

T8 T6

T5 T2

T20

T17

T12

T23

T21

T19

T18

T22

T7

T3T10

T15

T11

T14

T9

T13

T16

T8T6

T5T2

T20

T17

T12

Figure 12. Temperature distribution, calculated with FEMmodel (pc = 4.8 MPa, vac, TH = 150◦C)

the opposite temperature measurement positions of the con-tact area CI2. For the calculation of the TCR, the averagedtemperatures of the blade specimen (T13 & T16) and therotor specimen (T14 & T15) as well as the temperature de-pending thermal conductivity and the entering heat �ux atpair 1 are used. �ese calculation have been conducted forthe series of measurements with evacuated atmosphere andT̄H = 150◦C, to assume negligible heat losses and negligibleheat �uxes through the air pockets. �e calculation resultsare shown in Fig. 13 compared with those calculated by the

0 20 40 60 80 100Contact pressure [MPa]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

TC

RC

I2=T

CR

CI2;0

[!]

1D modelFEM model

0 3000Rotational speed [rpm]

Figure 13. Comparison of thermal contact resistance (TCR)calculated by 1D & FEM model (vac, TH = 150◦C)

0 20 40 60 80 100Contact pressure [MPa]

0

0.2

0.4

0.6

0.8

1

1.2

_ Q=

_ Q0[-] CI2, 1D model

CI2, FEM modelAP, FEM modelAP & CI2, FEM model

0 3000Rotational speed [rpm]

Figure 14. Comparison of heat �uxes calculated by 1D &FEM model (vac, TH = 150◦C)


use of the numerical FEM model. It can bee seen that theTCR values of the numerical FEM model are higher than thatone of the 1D approach. �is deviation can be explained bythe neglected heat �uxes through the air pockets by the 1Dmodel. Both, the results of the FEM and the 1D model, are inthe same range. �e advantage of the 1D model is the veryfast calculation time. Whereas, the CHT model has a higheraccuracy.

Figure 14 shows the di�erent heat �uxes through the airpockets (AP) and contact interfaces (CI) calculated with theFEM and 1D model. �e results con�rm the hypothesis thatthe deviation between 1D and CHT model is caused by theheat transfer through the air pockets. �e transmi�ed shareof radiation energy decreases with increasing contact pres-sure. �us, the radiation in�uence decreases with decreasingTCR, which was predicted previously in Fig. 7.

6. CONCLUSION�e present paper deals with an experimental set-up for ap-plied investigations of the thermal contact resistance (TCR)at the blade-rotor-connection in a steam turbine. �erefore,a test rig was designed, which is able to measure the temper-ature at 26 di�erent measurement positions within a rotorand blade specimen. �e ambient pressure can be reducedfor minimal heat losses and increased measurement accuracy.For the quanti�cation of the measurement uncertainties, anuncertainty analysis has been conducted. �e relative errorof the relevant temperature measurements (T1 - T26) is lessthan 0.6%.

First measurements with a specimen with radial contactinterfaces were conducted and introduced. �e results showa distinct trend with increasing contact pressure and increas-ing temperature level. For the determination of the TCR an1D approach as well as a numerical FEM model were devel-oped. �e results and a comparison of both models werepresented. �e TCR reaches high values with decreasingcontact pressure. �us, the assumption of full metal contactbetween the blade root and the rotor especial during opera-tions with low rotational speed, such as start-up / cool-downor warm-keeping / pre-warming, is not justi�able.

In future investigations an analytical approach for theTCR will be developed based on the conducted and furthermeasurements. �erefore, the in�uence of the contact surfaceproperties (roughness and oxidation layer) will be analyzed.�e �nal analytical correlation of the TCR will be integratedinto a turbine model [cf. [15]] for simulating steam turbinewarm-keeping operation.

ACKNOWLEDGMENTS�e authors gratefully acknowledge GE Power for their sup-port and permission to publish this paper.

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test rig for applied experimental investigations of the thermal...

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